March 14, 2006
The Non-Random Walk Theory - Persistency
by Damian Campbell

Non-Random price behavior is not a myth. It exists and if you are not exploiting it you should be. Here is a closer look...
The CET Capital investment strategies aim to exploit persistent price behavior of the small cap stock indices and mutual funds. While some of CET Capitals' methodologies are proprietary, exploiting persistent price behavior; which is the foundation of what we do is not. Persistency, as defined by Gil Blake, is a combination of volatility and historical reliability. Below I will summarize an interview in Jack Schwagers' book, The New Market Wizards, which eloquently describes how in the 1980's a successful money manager named Gil Blake capitalized on persistency. My aim is to demonstrate two ways of identifying non-random, persistent price behavior. The first will describe non-random price behavior in terms of probability. The second will show persistency in terms of compounded annual return and drawdown. My goal is to convince you that exploitable persistent trends have existed as far back as your grandparents can remember and they exist today. Simply put, you should be invested with a manager who exploits these trends.
The history of persistency
Gil Blake was one of the first money managers to exploit non-random price behavior and talk about it. Below is a summary of his interview from Jack Schwagers' book The New Market Wizards. The chapter is called "Gil Blake: The Master of Consistency".
Gil Blake was a mutual fund timer who was able to achieve gains of over 20 percent per year. Blake's life changed in the early 1980's when a friend presented him with evidence of non-random market behavior. When choosing which mutual funds to trade he "would rank each sector based on a combination of volatility and historical reliability, which he called persistency". He became so confident in monetizing these persistent trends that he took out four successive mortgages on his house over a three year period so he could invest more money in his strategy. When he started to examine managed sector funds he was amazed "that the daily average price change in a given sector had anywhere between a 70 percent to 82 percent chance of being followed by a move in the same direction the following day." One of the things that Blake said was, "If the odds are 70 percent in your favor and you make fifty trades, it's very difficult to have a down year". His high trading frequency eventually got him banned from Fidelity and was also a large influence on the introduction of what are now known in the mutual fund industry as early redemption fees. His successes were also a tremendous influence on CET Capital. I want to note here that with the introduction of high beta inverse mutual funds from fund families like ProFunds and Potomac hedging can be used instead of selling. As of March 2006 CET Capital is trading a short term strategy which incorporates hedging instead of selling, therefore actively trading these managed mutual funds is now once again possible.
Analyzing persistency
A more familiar way of looking at "Persistency of Price" (POP) is to think of it in terms of "winning streaks". Below POP is shown for consecutive up days ranging from two days (POP2) to six days (POP6) for three of the major US indices.

Start date of analysis: September 9, 1988. End date of the analysis: December 30, 2005. Statistics were compiled using FastTools analysis software and FastTrack data.
Simply put the Russell 2000 is the most persistent index in this group. An up close has a 62 percent chance of being followed by an up close in the same direction the following day (POP2), while the probability of having three up closes in a row is 39 percent (POP3). Like Blake, I look at it is like this, if you are trading something that has a 62 percent probability of closing up tomorrow if today is an up day and you are making between forty and sixty trades per year it will be difficult to have a down year.
Therefore if you simply buy on an up close and sell on a down close in the long run you capture the heart of the price move and beat buy and hold. Below there are two sets of charts which compare trading for persistency vs. using the buy and hold approach of the respective index from its inception. The top group of charts is thumbnails and will open to bigger charts if you click on them. These charts represent the simulated compounded growth of a $1000 using the above simulation rules for the S&P 500, NASDAQ 100 and our trading vehicle of choice the Russell 2000. The bottom table takes a closer look at each strategies compounded annual return (CAR), maximum drawdown and ulcer index (UI).
Trading for Persistency vs. Buy & Hold
Growth of $1000

Click to open larger image in new window.
A closer look at the statistics behind the strategies.

In each of these examples trading for persistency blows away buy & hold. Historically, using this simple approach not only increases your compounded annual return it reduced drawdown significantly. The point I want to drive home here is short term trading for persistency works and it works better on the more persistent indices (Russell 2000) then the less persistent indices (S&P 500), hence why CET Capital trades the Russell 2000. The point is you should have a manager who focuses on persistency in your portfolio.
Note: CET Capital uses this short term trading approach as one of our triggers in all of our Short Term strategies. We have also identified periods of time in which the markets are more persistent. Our job is to sit on the sidelines when the day to day consistency of the market is low and invest when it is high. To further capitalize on market persistency we have identified the best periods of time in which to use leverage.

Damian Campbell
Investment Manager
www.cetcapital.com
Copyright © 2006 Damian

14-March-2006
Probability, Markets, and Decision Making, by Victor Niederhoffer

"The theory of probability is at bottom nothing but common sense reduced to calculus: It enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which oftentimes they are unable to account. It teaches us to avoid the illusions which often mislead us. There is no science more worthy of our contemplation nor a more useful one for our system of education." -- P.S. Laplace, ~ 1800.
There is universal acceptance these days that knowledge of probability theory is useful in almost any field where decisions are made. The reason is that most of the things we are confronted with in life are not causal situations but common sense ones where our previous knowledge of circumstances and the intrinsic uncertainty of the situation calls for decisions based on probability. Thus, almost any scholarly field these days ranging from biology to economics to engineering to law where the relevance of evidence, physics, computer science, networks, linguistics, is replete with probabilistic reasoning. See "Current and Emerging Research Opportunities in Probability " for nice summary of this.
There is also a general appreciation that probability has as wide a range of application in terms of its practical range as geometry. However, unlike geometry, probability theory depends upon a different way of thinking, one that's not intuitive to most of us, and one where we commonly make more mistakes in reasoning than in any other field.
To improve my own understanding of probability theory, I have been reading some excellent books on it recently Understanding Probability Theory by Henk Tijms ( a book of interesting problems with rigorous but easy to conquer mathematical reasoning), Elementary Probability Theory with Applications, by Larry Rabinowitz (a book with practical problems with worked out problems that just requires good reasoning and is completely assessable to anyone who likes numbers), Why Flip a Coin? by H.W. Lewis (an elementary non-mathematical tract with a discussion of the wide ranging areas where decision making under uncertainty comes into play from dating to war), Probability Theory by E.T. Jaynes (a thoroughly profound and deep work that breaks new ground in a philosophy of reasoning and decision making with highly technical statistical discussions), and Probability and Random Processes by G. Grimmett and D. Stirzaker (a complete advanced modern text along the lines of Feller but more modern and up to date and accessible). All accomplish their goals, and are highly recommended for those interested in such goals.
Needless to say, probability theory is crucial to correct decision making in finance and markets. Thus, it is not at all unlikely that I would find that many of the classical probability problems have direct applications to markets that to my knowledge have not been fully explored. I will consider two of these below the secretary of Sultan's Dowry problem (a problem in sequential decision making, and the Monty Hall problem (a problem relating to revision of beliefs based on new information).
Let's start with the Sultan's Dowry problem. The situation here is that a commoner is given the chance to marry one of say eight sultan's daughters. Each has a different dowry. And each will be presented to the commoner one at a time, with a thumbs up or down decision that cannot be reversed. The situation also comes into play from the other side as the dating game problem with the lovely lady being presented sequentially with a dozen suitors. How is she to choose the one that she wants to marry with or will have the best sex with based on her previous experience. Or in more common terms, how does the boss choose the best secretary from a dozen that he's going to interview sequentially, or how dose he indeed travel from Austin to Dallas and decide how many gas stations to pass before choosing the one that has the lowest price.
Such problems are at the core that every market person is faced with. How does one decide when to sell a stock, especially if a need for money arises before the end of the period, or how does the day trader decide when to get out of his positions knowing that overnight positions are not accepted, or how does the pattern trader decide when to enter his trades given that he waits too long, he may miss the trade. How at a more general level does one pick the right time to sell premium of any kind considering that you'd like to sell at the high, but if you wait too long you might lose the whole thing.
The solution to such problems is very elegant and many of us in the office gained an appreciation for the closed form solution while the artful simulator, Mr. Downing, immediately went to the simulation solution and was able to work it out in about 30 seconds. (As an aside here, all modern books on probability theory suggest that the key to gaining an understanding of it is to work with random number generators on the computer to simulate the answers to the common problems. I would agree except to say that's it's even better to work it out by hand with a random number table for the simplest 1 or 2 element formulations of the problems)
The correct decision making to make is to go thru interviewing 3 daughters just to gain information and then to start searching for the first one with a higher dowry among the remaining 5.
The solution in brief starts with the knowledge that any daughter looked at has a chance of 1/8 to be the highest dowry of the 8 daughters. However, to correctly choose her, she must not only be the highest but the highest of the first three that you interviewed to form a base that had no chance of being chosen must be higher than the subsequent ones you interviewed and passed over because they did not contain a higher score.
Thus, after going thru 3 dowries, the chances that the fourth one will be highest and correctly chosen is 1 in 8. The chance that the fifth one will be highest and correctly chosen is 1/8 times the chance that the highest of the four previous scores came among the first 3, i.e. 1/8 x 3/4. The chance that the sixth one will be correctly chosen is 1/8 times the chance that that the daughter with the highest dowry was among the first 3 of the 5 daughters considered, i.e. 3/5 x 1/8. The chance that the seventh daughter will be correctly chosen is 1/8 times the chance the daughter with the highest dowry thru daughter 6 was among the first 3 of the six daughters previously considered, .i.e. 1/8x 3/6. The chance of winning by choosing the last daughter is the 1/8 chance that she's highest x the chance that the highest dowry of the first 7 was among the first 3, i.e. 1/8 x 3/7. In order to be correct, the commoner must choose the one and only that is highest of the 5 chances he has to be correct. Thus, each of the 5 chance calculations if exclusive and the correct answer for the probability of being correct is to add up the 5 probabilities. Such a sum has a beautiful closed form solution which for large numbers of daughters comes to 1/e (of course), or 0.37.
The application to when to put on a trade is rather direct. Divide the day into 8 intervals. Let 3 of them pass to give you a foundation for choosing the best of the 3 that you let go. Then choose the next one that gives you a better entry (lower if you want to buy, or higher if you want to sell). The chances that you will be right according to the closed form solution verified by Mr. Downing is about 0.40. Indeed, the chance of finding the daughter with the greatest dowry out of 8 daughters is 0.32 if you stop after the first daughter and then look for the next one higher, 0.39, if you stop after the second daughter, and look for the next one higher, 0.41, for 3, 0.39 for 4, 0.32 for 5, 0.24 for 6, and 0.12 for 7. Thus, it doesn't make much difference if you wait to interview two, three, or four secretaries or brides or lovers out of 8, before you begin to clear for the action of choosing the next one that's higher. But there's quite a fall off if paralyzed by the fantastic potential of it all you wait for 5, 6, or 7 of the beauties to pass you by. A more realistic version of this problem might take into account the cost in time of interviewing all the candidates, and the chance that conditions might change.
Such reasoning is easily transferable to a wide range of trading decisions during the fray. (to be continued with the Monte Hall problem applications).

Dentro de mi rutina diaria, en la que además de correr mis estrategias y chequear las señales que se pueden venir durante la batalla diaria, también incluyo un recorrido a través de internet de páginas que contienen información relevante.
Aquellas páginas que son de noticias, las paso más rápido, creo que las noticias son ruido y es como ver en el retrovisor del auto. Si son señales y no ruidos, mis posiciones ya lo reflejaron y sólo me queda ver que su efecto esté dentro de mis rangos de acción. Por lo anterior, no compro el períodico, aunque chequeo como dije rápidamente los encabezados.
Creo que si existe señal en internet y por ello la uso. En un blog pasado, de los primeros, listo los Blogs, Podcasts y Radio Internet que leo, uso y oigo. Pueden interesarle.
En mi rutina de hoy me tope con dos lecturas que las compartiré con uds. A pesar de que el presente Blog es en español, la gran mayoría de lectura de la profesión está en inglés.
No saber inglés en estos tiempos en nuestra profesión es como ir a la batalla con mapas con indicaciones en japonés o peor aún sin ellos. Lo anterior no garantiza pérdida pero definitivamente es algo que juega en contra o por lo menos le dá una ventaja a nuestros competidores.
El primer artículo escrito por Victor Niederhoffer, uno de mis favoritos, en donde ejemplifica el uso de probabilidades en el mercado. En él recomienda libros teóricos que nos pueden ayudar en el tema, pero ejemplifica con una historia cómica acerca de la elección de una mujer en un harem. Lo interesante es la analogía con trading es muy relevante.
El segundo, es un sistema de trading. En él estudia la persistencia de los movimientos de los principales indices. Su conclusión se parece a lo que he estado escribiendo recientemente. Concluye que el Nasdaq 100 y SPX no tienen propiedades de tendencia tan relevantes como el Russell 2000.
Me gustaron ambos artículos porque se parece mucho al enfoque que utilizo para trading. Identificación de eventos que se repiten, los cuales luego de recolectarlos son analizados estadísticamente para ver si sus propiedades son significativas.